688640064 has 112 divisors (see below), whose sum is σ = 2090245248. Its totient is φ = 196005888.

The previous prime is 688640053. The next prime is 688640083. The reversal of 688640064 is 460046886.

It is a tau number, because it is divible by the number of its divisors (112).

It is a Harshad number since it is a multiple of its sum of digits (42).

It is a junction number, because it is equal to n+sod(n) for n = 688639998 and 688640025.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 419854 + ... + 421490.

It is an arithmetic number, because the mean of its divisors is an integer number (18662904).

Almost surely, 2^688640064 is an apocalyptic number.

688640064 is a gapful number since it is divisible by the number (64) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 688640064, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1045122624).

688640064 is an abundant number, since it is smaller than the sum of its proper divisors (1401605184).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

688640064 is a wasteful number, since it uses less digits than its factorization.

688640064 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1972 (or 1962 counting only the distinct ones).

The product of its (nonzero) digits is 221184, while the sum is 42.

The square root of 688640064 is about 26241.9523663923. The cubic root of 688640064 is about 883.0746717512.

The spelling of 688640064 in words is "six hundred eighty-eight million, six hundred forty thousand, sixty-four".